Sam Sanders - Plato and the foundations of mathematics
|Starts:||15:00 16 Oct 2019|
|Ends:||15:00 16 Oct 2019|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
|Who is it for:||University staff, External researchers, Current University students|
Sam Sanders joins us for the Logic Seminar.
Plato is well-known in mathematics for the eponymous foundational philosophy ‘Platonism' based on ideal objects. Plato’s 'allegory of the cave' provides a powerful visual illustration of the idea that we only have access to shadows or reflections of these ideal objects. An inquisitive mind might then wonder what the current foundations of mathematics, like e.g. Reverse Mathematics and the associated Goedel hierarchy, are reflections of. In this talk, we show that the aforementioned are reflections of a much richer higher-order hierarchy under the canonical embedding of higher-order into second-order arithmetic. We make use of well-known generalisations e.g. nets versus sequences and the gauge integral versus Riemann's integral. Philosophical discussion is kept to a minimum.
Organisation: University of Leeds
Travel and Contact Information
Frank Adams 1
Alan Turing Building